Moses saw the goodness of God “pass before him”, but that goodness was expressed in the proclamation of the divine name. What Moses heard were the divine attributes, grace and mercy, articulated with the imperfect-future I will be gracious and I will show mercy (Exod 33:18-20), thereby establishing the hope of future God manifestation (cited by Paul in Rom.9:15 also using the future tense). The echo and allusion is with Exod 3:14 and I will be who I will be.
The phrase I will be who I will be begs the question: Who will God be? The covenant promise vouched safe to David answers the question:
He shall be to me a Son 2 Sam.7:14 (KJV)
This is an obvious allusion to the texts of Exod 3:14 and Exod 33:18-20 – the son would manifest the qualities and character of the Father (“to him”). This passage is quoted in the future tense in Hebrews, “I will be to him a Father, and he shall be to me a Son” (Heb 1:5), within the context of a discussion of inheriting a more excellent name (Heb 1:4).
Perhaps this theology of God manifestation is best expressed in a formulation used by the apostle Paul in 1 Cor.15:8-10 which has multiple echoes with Exodus 3:
And last of all he was seen (cf. ‘appeared’—the same word is used in Acts 7:30 in the description of the burning bush incident) of me…For I am the least of the apostles….but by the grace of God I am what I am…yet not I but the grace of God which was with me. 1 Cor 15:8-10 (KJV)
The context of the passage (1 Cor 15:4) is redemption, salvation (cf. Exod 3:7-10, 17) and resurrection. Paul was an apostle (=“sent one” cf. “send” in Exod 3:10, 12, 13, 14, 15), and God promised to be with him as with Moses (Exod 3:12).
Paul affirms I am what I am, echoing I will be who I will be in Exod 3:14. He uses the present tense I am, because he fulfils the terms of I will be who I will be—God was manifested through the Spirit in him. Jesus had said that he was a “chosen vessel to bear my name” (Acts 9:15).
In a similar fashion the blind man, whose sight was restored (like Saul’s), could say: I am (John 9:9). The blind man uses exactly the same syntactic expression for which Christ was almost stoned in John 8:58—yet he was not claiming to be God. Jesus explained that the blind man had his condition so that “the works of God might be made manifest in him” (John 9:3). Hence, the blind man was inspired to say I am in order to show how he fulfilled the terms of the promise in I will be who I will be.
The name of Jesus is an abbreviated form of Yahweh prefixed to the Hebrew verb for “to save”—Yahshua. This name becomes Iesous in the Greek and is coupled with the third person future form “he shall save” in Matt 1:21-23,
…and thou shalt call his name Jesus: for he shall save his people from their sins…and they shall call his name Immanuel….God with us. Matt 1:21-23 (KJV)
Matthew’s narrative at this point is a paronomasia that explains ‘Jesus’ in terms of redemption (“save”) and fellowship (“with”). Isaiah called the Messiah “Immanuel” or “God with us” which picked up on the Exodus motif, “Certainly, I will be with thee” (Exod 3:12). Hence, Jesus was to claim that “I am come in my Father’s name” (John 5:43) and that “I have manifested thy name” (John 17:6). He did this insofar as he too was a fulfillment of I will be who I will be.